One thing which Germany learned from the Third Reich era was that plebiscites are dangerously vulnerable to propaganda. When the likes of Goebbels promised to restore national strength, of course a lot of people believed him - but they didn't know the true picture as they only had his propaganda and the bully boy enforcement activities of the Sturmabteilung breaking up opposition meetings to persuade them to vote for their new chancellor.
So it wouldn't have been possible to have held a plebiscite, such as Cameron's referendum, in Germany - because they are now illegal. While the mood of the people can influence, the constitution allows only the elected government to makes decisions on national policy.
The propaganda, spin and lies of the likes of Johnson, Gove and Davis hoodwinked many into voting as they did, because they weren't given the true picture - as is now becoming ever more obvious.
As for Davis using RAF corgi-carriers to take him to various meetings? Only if the door-to-door time is critical should that be acceptable, provided that the government actually pays the true cost of such flights.